Methods
Latent Atlas asked whether a satellite foundation model's embeddings know something about Europe's surface climate that a stack of hand-crafted covariates does not. At 6 km they do not. The rest of the site maps what they do encode.
- The comparison: the embeddings predict daily maximum temperature 4.2% worse than the covariates on RMSE.
- The correction: a pooling defect was fixed and the comparison run again, with the same answer.
- Other products: what the forest, solar and wildfire cards are scored against.
- Data: every source, with its credit.
The Six-Arm Comparison
Every arm predicts COSMO-REA6 daily maximum temperature at 6 km over Europe, with ERA5 as the coarse input. The arms differ only in the static feature block appended to that input, so two rows differ only in how they represent place. Each is a quantile regression fitted per fold and scored on the fold it never saw. The folds are contiguous spatial blocks, because on an autocorrelated field a random split leaves every held-out cell's neighbours in the training set. Iberia is held out entirely and never enters the pooled statistic.
| Arm | Static features | RMSE, daily maximum (K) |
|---|---|---|
| bilinear | none, the interpolation floor | 1.860 |
| cov | hand-crafted covariates | 1.469 |
| aef | AlphaEarth, 64 dimensions | 1.531 |
| aef_cov | both | 1.468 |
| clay | Clay v1.5, per-fold PCA | 1.621 |
| mosaiks | random texture features over the covariate rasters | 1.480 |
Result
Pooled over 5 held-out spatial folds, the embeddings are 4.2% worse than the covariate stack on RMSE and 4.3% worse on CRPS.
Adding the embeddings to the covariates barely moves the error, and random texture features drawn over the covariate rasters come close to the covariates themselves.
The covariates are elevation, its standard deviation and topographic position index, slope, northness and eastness, distance to the coast, built-up, tree and water fraction, population density, built height, and the pixel count behind each source raster. The norms card measures what pooling from 40 m to 6 km does to the length of an AlphaEarth vector.
The Corrected Measurement
AlphaEarth stores each component as an int8 code under a signed square-root companding. The first version of this pipeline averaged the raw codes when it pooled tiles onto the 6 km grid, and the mean of companded codes is not the code of the mean vector, so every pooled direction was wrong. The rebuilt cube de-quantises before averaging and renormalises once the mosaic is assembled. Apart from the defective-cube figures quoted below, every continental-grid number on this site comes from it. The fix has its own page.
On the defective cube the embeddings were 4.17% worse than the covariates on RMSE and 4.31% worse on CRPS. On the corrected cube they are 4.19% and 4.32% worse.
Cards Measured Against Other Products
The forest, solar and wildfire cards score the embedding against a product someone else made. Each scores only places kept out of training and names its product in the sentence that gives the result. A score is agreement with that product, errors included, and validates neither the product nor the embedding.
The Year Before the Dieback
FCCL_DE_P1M, DLR's monthly 10 m canopy-loss map of Germany under CC BY 4.0 (Thonfeld et al. 2026). EFDA v3.0.0 for the disturbance agents.
Reading only the 2018 embedding, a model ranks the stands FCCL_DE_P1M records as lost in 2019 to 2021 better than 12 hand-crafted covariates do, in every one of 4 German forests. Averaged to the covariates' coarser 100 m it keeps the lead in 3 of them, but not in the Black Forest.
Watching Germany Go Solar
MaStR, the Bundesnetzagentur's Marktstammdatenregister, extract 20260921.
The embedding dates a solar park's build to within a year of the year MaStR registers for 81.0% of held-out parks. The best single year, guessed for every park, gets 65.0%.
How Long a Wildfire Is Remembered
EFFIS burnt areas, the Joint Research Centre's MODIS burnt-area perimeters, extract 20260923.
On fires far from any it trained on, the embedding tells burnt ground from its unburnt neighbours with an AUC against EFFIS of 0.9203 a year after the fire. By 3 years its interval overlaps the one the landscape alone scores before any fire (0.6488 to 0.7784).
How Cities Change describes what the embedding does over a city at 10 m and measures nothing. The remaining cards map the embedding itself: its neighbours, its outliers, its geometry, what it says about summer heat and how it moves from year to year.
Data Sources
Embeddings
- AlphaEarth Foundations annual embeddings, Google and Google DeepMind, CC BY 4.0, via Source Cooperative. Read from the 40 m overviews for the continental grid and at the native 10 m for every card below it.
- Clay v1.5, for the comparison's clay arm.
The Temperature Comparison
- COSMO-REA6 reanalysis, Deutscher Wetterdienst: the target.
- ERA5 reanalysis, ECMWF. Contains modified Copernicus Climate Change Service information.
- Copernicus DEM, © DLR e.V. and © Airbus Defence and Space GmbH, provided under COPERNICUS by the European Union and ESA: elevation and terrain.
- ESA WorldCover 2021 v200, © ESA WorldCover project, contains modified Copernicus Sentinel data (2021) processed by the ESA WorldCover consortium: built-up, tree and water fraction.
- GHS-POP and GHS-BUILT-H R2023A, European Commission Joint Research Centre: population density and built height.
- Natural Earth coastline, public domain: distance to the coast.
Products the Cards Are Scored Against
- FCCL_DE_P1M canopy loss, DLR/EOC (Thonfeld et al. 2026), CC BY 4.0.
- European Forest Disturbance Atlas (EFDA) v3.0.0, CC BY 4.0, disturbance agents.
- Marktstammdatenregister, Bundesnetzagentur, extract 20260921.
- EFFIS burnt areas, European Commission Joint Research Centre, extract 20260923.
Imagery and Maps
- Sentinel-2 L2A, through Earth Search and Microsoft's Planetary Computer. Every Sentinel-2 view on the site contains modified Copernicus Sentinel data, and on the Unusual, Doppelgängers, wildfire and solar tiles of the front page and their link previews that data is from 2018-2023.
- Imagery on the Unusual, Doppelgängers, Walk and Drift cards, in the insets, the thumbnail strips and the Drift map's Ground view: Esri World Imagery (Esri, Vantor, Earthstar Geographics, and the GIS User Community).
- Place names: GeoNames (CC BY 4.0).
- Borders: © EuroGeographics, via Eurostat GISCO.
- Coastlines, land masks, country outlines and the solar map's towns: Natural Earth, public domain.
Prior Work
Searching an embedding for look-alike places is not new. Google's Earth Engine has a similarity-search app, the yagays/alphaearth-embeddings project explores the same embeddings, and Terrapattern did it for aerial imagery before either. The Unusual, Walk and Doppelgängers cards run that idea over Europe at 6 km.